Visas and visitor's passes
Visas can be obtained in advance from any Kenyan embassy, consulate or high commission (sometimes from a British embassy in countries where Kenya has no diplomatic representation). Visas normally take 24-48 hours to process, require two passport-size photos and usually an air ticket out of the region (not just to Uganda or Tanzania). This requirement is usually waived if the embassy is satisfied of your alternative arrangements or financial responsibility. A single-entry visa costs £35/$50 and is valid for three months. Multiple entry visas cost roughly double that. Remember that Kenyan diplomatic missions are closed on Kenyan public holidays. Transit visas (valid for seven days) can be bought on arrival for $20. Visas are normally valid for entry within three months of the date of issue.

It's possible to get a visa on arrival at the airport (sterling or dollars cash only), though it's best avoided if you're arriving at night. Although this is generally a hassle-free formality, it does leave you open to potential problems caused by corrupt officials preying on your fear of being refused a visa. It also generally requires you to stand in line and can take up to an hour, so if you do decide to take this option, get off the plane quickly.

On arrival in Kenya you'll be issued with a visitor's pass usually limiting the length of stay to three months, though various factors may determine the length of time granted, including your appearance, how much money you have and (fortunately) how long you actually want to stay.

Your visa allows re-entry to Kenya after visits to Uganda or Tanzania (assuming of course you have a visa for these countries). For other trips outside Kenya, you'll need to reapply for a visa to get back in.

Customs
Duty free allowance is one bottle of spirits or wine, and one carton of 200 cigarettes or 50 cigars or half a pound of tobacco.

If you're stopped at the customs benches, you will normally be asked if you have any photographic equipment, video camcorders, cassette players and so on. Unless you're some kind of professional, with mountains of specialist gear, there shouldn't be any question of paying duty on personal equipment, though some customs officers like to make notes of it all in your passport to ensure it is re-exported. If you have friends in Kenya, however, and are taking presents for them, you are likely to have to pay duty if you declare the items. Even if you have nothing to declare, corrupt customs officers may ask you for a bribe before clearing you: you can of course refuse, and they will usually give up on you after half an hour; alternatively, you can kick up a fuss